Controlling a modular converter in two stages

ABSTRACT

A modular converter having a plurality of converter modules for converting an input voltage into an output voltage to be supplied to a load by receiving a control input reference vector, a control input vector and a control input parameter vector; determining a control output reference vector from the control input reference vector, the control input vector and the control input parameter vector in a first control stage; and controlling the converter modules by generating switching signals based on the control output reference vector in a further control stage.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §120 to Internationalapplication PCT/EP2013/067791 filed on Aug. 28, 2013, designating theU.S., and claiming priority to European application 12181995.7 filed inEurope on Aug. 28, 2012. The content of each prior application is herebyincorporated by reference in its entirety.

FIELD OF THE INVENTION

The invention relates to a method for controlling a modular converter, acontroller for controlling a modular converter and a modular converterwith such a controller.

BACKGROUND OF THE INVENTION

Modular converters and in particular modular multi-level converters(M2LC) are used for synthesizing voltages to be supplied to a load, forexample an electrical motor or an electrical grid. The modular structureof modular converters offers a number of advantages such as modularity,scalability, high output voltage and low output current distortions.

A standard approach to achieve closed-loop control of a modularconverter is to divide the control problem into two hierarchical upperand lower stages or layers. The upper, first stage may be based onvector control with a modulator. The vector control scheme may operatein a dq reference frame. By manipulating the voltage reference, which isinput to the modulator, closed-loop control of load currents may beachieved. For example, carrier-based pulse width modulation (PWM) orspace vector modulation (SVM) may be used in a modulator. Circulatingcurrents and/or an energy balance within converter branches may beaddressed by adding additional control loops.

The lower control stage utilizes the redundancy in the converter states(i.e. groups of switching states that produce the same line to linevoltage) in order to balance the capacitor voltages. The capacitorvoltages may be sorted in an ascending/descending order of their voltagevalues. For a charging current the capacitors with the lowest voltagesmay be selected first, and conversely, the capacitors with the highestvoltages may be prioritized for discharging currents.

DESCRIPTION OF THE INVENTION

It may be objects of the invention to simplify the development ofcontrollers of modular converters, to provide more flexibility in thecontrol objective of a modular converter, to minimize switching lossesof a modular converter and/or to minimize the response time of acontroller of a modular converter.

These objects are achieved by the subject-matter of the independentclaims. Further exemplary embodiments are evident from the dependentclaims and the following description.

An aspect of the invention relates to a method for controlling a modularconverter.

The modular converter comprises a plurality of converter modules thatmay comprise semiconductor switches and at least one capacitor. Themodular converter is adapted for converting at least one input voltageinto at least one output voltage to be supplied to a load. For example,the modular converter may connect a grid with an electrical rotatingmachine like a motor or a generator or may interconnect two electricalgrids. The modular converter may be a modular multi-level converter. Themodular converter may be an AC-to-DC converter, a DC-to-AC converter, oran AC-to-AC converter.

According to an embodiment of the invention, the method for controllingthe converter comprises the steps of: receiving a control inputreference vector, a control input vector and a control input parametervector; determining a control output reference vector from the controlinput reference vector, the control input vector and the control inputparameter vector in a first control stage (or layer); and controllingthe converter modules by generating switching signals from the controloutput vector in a further control stage or control layer. The differentcontrol stages or control layers may be implemented in differentcontrollers.

The control method may supersede the vector control scheme as describedabove. The control input reference vector (i. e. a reference vectorinput to the first control stage) may be a current reference vector andthe control input vector may be an actual current vector that may havebeen estimated or measured from actual currents and/or voltages in themodular converter.

It has to be noted that a vector may contain only one entry, i.e. that avector comprises only a value. However, usually, a vector may contain atleast two entries.

The control output reference vector (i.e. a reference vector output fromthe first control stage) may be a voltage reference vector that is inputto the next control stage, which may be a modulator. In other words, thevariable manipulated by the first control stage may be a real-valued(voltage) reference for a modulator.

According to an embodiment of the invention, the control outputreference vector is determined by: predicting at least one future stateof the modular converter with a prediction model of the converter;optimizing the at least one future state with respect to an objectivefunction; and determining the control output reference vector from thefuture state.

Summarized, the first control stage is adapted for predicting theevolution of an internal state vector of the modular converter (andoptionally the load) and of the control output reference vector and foroptimizing the control output reference vector such that the futurestate, or a subset of it, approaches the control input reference vectorand that further control objectives like, for example, minimal switchingefforts or keeping some variables within some constraints, are achieved.In such a way, a next control output reference vector may be determinedfrom which the next switching state can be derived.

The prediction model may be a mathematical model of the modularconverter and optionally the load that is implemented in the firstcontrol stage. The prediction model may be adapted for calculating thefuture state of the converter based on an actual state of the converter.An (actual and/or future) state of the modular converter may comprisecurrent values and/or voltage values of the modular converter. Theactual state may comprise the control input vector and the control inputparameter vector. The future state may comprise an evolution of thecontrol input vector and the control input parameter vector.

It has to be noted that the prediction horizon of the prediction modelneeds not be one time step but may have any length. The prediction modelmay allow the first stage to predict the system response of controlactions, using a prediction horizon of any length. The model may begiven in state-space form.

A state of the modular converter may be any vector of quantities relatedto the evolution of currents and/or voltages in the modular converter(and optionally the load). A state or state vector of the converter maycomprise at least one of an upper and lower branch current and/orvoltage and a DC link current and/or voltage, an output current and/orvoltage and a circulating current. All these voltages and/or currentsfor an actual time step may be measured in the modular converter or maybe estimated from other quantities. These voltages and/or currents maybe used for determining, estimating and/or calculating the future stateof the modular converter.

The objective function may be a real-valued, scalar function implementedin the first control stage. The objective function may penalizedifferences between the control input reference vector at a time stepand the predicted evolution of the control input vector at this timestep. The objective function may be based on a cost value associatedwith switching costs of the converter modules. In such a way, a scalarcost value or performance index is associated with the predicted controlactions and the corresponding predicted system response. For example, apenalty on manipulating a commanded branch voltage may be used, as wellas a penalty on a predicted current error (for example a differencebetween the input current reference vector and the predicted evolutionof the input current vector).

The first stage may minimize the objective function with respect toconstraints and the dynamical evolution in time of the prediction model

Summarized, in the first stage, the dynamics of the modular convertermay be predicted, which may result in an optimal sequence of controlactions.

All the control stages of the method may be implemented in a controllerof the modular converter. This controller may be adapted formanipulating the branch voltages of the modular converter such that thefollowing control objectives may be achieved:

Currents associated with the control input vector may be regulated alongtheir given references (associated with the control input referencevector). For example, there may be five currents to be regulated,assuming a three-phase modular converter with a load, whose star pointis not connected to ground. These five currents may be either fivebranch currents (the sixth branch current depends on the other fivecurrents) or two load currents plus three circulating currents.

During transient operating conditions, including step changes in theload current references and in the presence of external disturbances,very short current response times may be achieved.

Constraints on the currents may be imposed and met, such as upperconstraints and rate constraints on the branch, load, circulating andDC-link currents. Moreover, per phase leg, the sum of the upper andlower commanded branch voltages may be less than the DC-link voltage.Additional constraints on voltages and currents may be imposed, forexample regarding the load.

According to an embodiment of the invention, the control input referencevector is a current reference vector and the control input vector is anactual current vector. The control input parameter vector may be anactual voltage vector, i.e. a vector of actual determined and/ormeasured voltages values. The control output reference vector may be avoltage reference vector. The control method may be a method controllingcurrents by manipulating (branch) voltages.

According to an embodiment of the invention, a sequence of future statesor future state vectors is predicted for a plurality of time steps inthe future, i.e. over a prediction horizon with a length of more thanone time step. The control output reference vector may be determinedfrom the next future state associated with the next time step, forexample by solving the underlying mathematical optimization problem,which may be a quadratic program (QP). Moreover, a receding horizonpolicy may be used for determining the next control action for the nexttime step. This may mean that only the first element of the optimalsequence of control actions is implemented, i.e. used for driving theswitches of the converter modules. At the next time step, newmeasurements may be obtained and the optimization problem may be solvedagain over a shifted prediction horizon.

According to an embodiment of the invention, the prediction model isbased on linear equations relating voltages and/or currents at a timestep with voltages and/or currents at a next time step. For example, theequations may be derived from the topology of the modular converter andKirchhoff's laws.

According to an embodiment of the invention, the prediction modelcomprises a model of the converter modules and/or a model of the load.For example, the prediction model may model capacitors of the convertermodules and may be adapted to predict an evolution of the capacitorvoltages. The prediction model may comprise a model of the load and maybe adapted to predict an evolution of a load (grid) voltage. Models ofhigher order load systems, including AC machines, loads with filters,loads with long cables, loads with transformers, etc. may be included inthe prediction model.

According to an embodiment of the invention, the method furthercomprises the step of: compensating a time delay caused by thedetermination of the control output reference vector by predictingcurrents and/or voltages, for example the control input reference vectorand the control input vector, at the next time step with the use ofactual currents and/or, for example the actual control output vector,the actual control input reference vector and the actual control inputvector. The computation of the next control action usually takes most ofthe time of one time step. By starting the prediction with voltagesand/or currents predicted for the next time step, the control outputreference vector may be calculated such that the control action (i.e.the switching commands) are applied at the time, the prediction hasstarted from.

According to an embodiment of the invention, the objective functionminimizes a change in an evolution of the control output referencevector over time. For example, in the case the control output referencevector comprises voltages, the objective function minimizes voltagechanges in the evolution of these voltages over time. For example, theobjective function may comprise a term in which a norm is applied to thedifference between two consecutive control output reference vectors.

According to an embodiment of the invention, the objective function isbased on a quadratic norm. In such a way, components of the current/andor voltage vectors may be weighting differently. For example, thecontrol input vector may comprise branch currents, and circulatingcurrents, which may be weighted with different weights. In this case,solving the prediction model may result in a quadratic programmingproblem.

According to an embodiment of the invention, the objective function isbased on a linear norm. In this case, solving the prediction model mayresult in a linear programming problem, which may be fast to solve.

According to an embodiment of the invention, the method furthercomprises the step of: determining a voltage vector from the controloutput reference vector in a second control stage with a modulator; andcontrolling the converter modules by generating switching signals fromthe voltage vector in a third control stage. The control method may beapplied in a modular AC-DC, DC-AC and AC-AC converter with a modulator.

According to an embodiment of the invention, the method furthercomprises the step of: controlling the converter modules by generatingswitching signals from a rounded control output reference vector. Thevoltage reference vector input to the third control stage may begenerated by only rounding the output reference vector (for example avoltage reference vector). In such a way, the switching signals may begenerated directly from the output reference vector without a modulator.

For modular multi-level converters, the number of converter modules perbranch may be very high. A total branch voltage, which may be defined asthe sum of the capacitor voltages of module capacitors connected to thebranch, may then be approximated to be real-valued, rather thandiscrete.

In such a modular multi-level converter each converter modules of themodular multi-level converter comprises two power connectors, at leasttwo power semiconductors and a capacitor, wherein the power connectorsare short-circuited in a first switching state of the powersemiconductors and are connected to the capacitor in a second switchingstate of the power semiconductors.

Within a branch of the modular multi-level converter the convertermodules are serially connected by their power connectors.

According to an embodiment of the invention, the method furthercomprises the step of: detecting a converter module with a fault;short-circuiting the detected converter module; and removing theshort-circuited converter model from the prediction model. The controlmethod may use an automatic reconfiguration of the prediction model,when the topology of the modular converter changes.

For example, the converter modules of the modular converter and/or theload may be monitored in real-time. If a converter module fails and itsterminals are shorted to bypass it, the number of converter modulesavailable may be automatically updated and the internal prediction modelof the controller may be adjusted accordingly. As a result, the controlmethod may take the fact that some modules might be shortened intoaccount and may use switching actions that, within the physicallimitations of the converter, compensate for these shortened modules.Similarly, if a fault, disturbance and/or imbalance etc. occurs at theload, the prediction model is updated accordingly, too, and thecontroller compensates for this.

A further aspect of the invention relates to a controller forcontrolling a modular converter, which is adapted to perform the firststage of the control method.

For example, the control method may be implemented on any computationalhardware including DSPs, FPGAs, CPUs and processor cores. Also the otherstage of the control method may be implemented in a separate controller.

According to an embodiment of the invention, the controller is adaptedto perform the following steps: predicting at least one future state ofthe modular converter with a prediction model of the modular converter,wherein the prediction model is adapted for calculating the future stateof the modular converter based on an actual state of the converter, astate of the modular converter comprising current values and/or voltagevalues of the modular converter and/or load; optimizing the at least onefuture state with respect to an objective function, in particularsubject to constraints and the dynamical evolution of the predictionmodel, wherein the objective function is based a cost value associatedwith switching costs or an switching effort of converter modules of themodular converter; and determining a control output reference vectorfrom the future state.

A further aspect of the invention relates to a computer program that,when being executed by a processor, is adapted to perform the steps ofthe method the controller is adapted to perform and/or the steps of themethod as described in the above and in the following. A further aspectof the invention relates to a computer-readable medium on which such acomputer program is stored.

A computer-readable medium may be a floppy disk, a hard disk, an USB(Universal Serial Bus) storage device, a RAM (Random Access Memory), aROM (Read Only memory) and an EPROM (Erasable Programmable Read OnlyMemory). A computer-readable medium may also be a data communicationnetwork, e.g. the Internet, which allows downloading a program code.

A further aspect of the invention relates to a modular converter forsupplying a load with electrical voltages and/or currents.

According to an embodiment of the invention, the converter comprises aplurality of converter modules comprising semiconductor switches and acapacitor; a first controller as for performing the first stage of thecontrol method as described in the above and in the following, the firstcontroller generating a control output reference vector; and a furthercontroller for generating switching signals for the converter modulesbased on the control output reference vector.

According to an embodiment of the invention, the modular converter is amodular multi-level converter.

It has to be understood that features of the method as described in theabove and in the following may be features of the controller and/or themodular converter as described in the above and in the following.

Summarized, a method and a controller for controlling a modularconverter are described, which may use the concepts of model predictivecontrol (MPC). The controller may be seen as a model predictive currentcontroller (MPCC), which may be adapted for regulating the branch, phaseand/or circulating currents around their given references, bymanipulating the total (continuous-valued) branch voltages. Uppercurrent constraints as well as rate constraints may be addressed by theMPC method. The current references may be provided by an outer loop. Amodulator may be used to translate the branch voltage commands tointeger numbers, which refer to the number of modules per branch beingturned on. A subsequent balancing method may be used to maintain thecapacitor voltages around their references and to decide on theindividual modules being turned on and off.

The proposed MPC method may be used to address a current control problemof modular multi-level converters with a large number of convertermodules per converter branch. The controller may achieve very shortresponse times during transients and may require only a modestcomputational power. The MPC method may be used to provide fast torquecontrol for a modular multi-level converter driving an AC rotatingmachine.

The method may be used for all applications of a modular multi-levelconverter, including variable speed drives, high-voltage direct currenttransmission, flexible AC transmission systems, static synchronouscompensators, grid-interfaces for battery energy storage systems orphotovoltaic modules, traction applications, etc. The control method ishighly flexible allowing one to incorporate and address differentcontrol objectives and operation requirements.

These and other aspects of the invention will be apparent from andelucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject-matter of the invention will be explained in more detail inthe following text with reference to exemplary embodiments which areillustrated in the attached drawings.

FIG. 1 schematically shows a modular converter according to anembodiment of the invention.

FIG. 2 schematically shows a converter module for a modular converteraccording to an embodiment of the invention.

FIG. 3 schematically shows a controller for a modular converteraccording to an embodiment of the invention.

FIG. 4 shows a flow diagram for a method for controlling a modularconverter according to an embodiment of the invention.

FIG. 5 schematically shows a prediction model according to an embodimentof the invention.

FIG. 6 shows a diagram with sequences of control actions and predictedoutput sequences according to an embodiment of the invention.

In principle, identical parts are provided with the same referencesymbols in the figures.

Detailed Description of Exemplary Embodiments

FIG. 1 schematically shows a modular converter 10 with three converterphase legs 12 that interconnect a DC link 14 with an active three-phaseresistive-inductive (RL) load 16. Each of the phase legs 12 comprises anupper and a lower branch 20 interconnecting the positive and negativesides of the DC link 14 with one phase of the load 16. The modularconverter 10 is a modular multi-level converter with n=2series-connected converter modules 22 per branch 20.

In general, the modular converter 10 may comprise converter modules 22,M_(pq), with pε{a, b, c} and qε{1, 2, . . . n}, where n is the number ofconverter modules 22 per phase leg 12. The modular converter 10 maycomprise any number of converter modules 22 per phase leg 12. Eachbranch 20 comprises n/2 modules 22, a resistor R, that models conductionlosses and a branch inductor L.

The DC link 14 is shown with a DC supply inductor L_(dc) and a resistorR_(dc) that model the parasitic inductance and resistance, respectively.The modular converter 10 may provide n+1 voltage levels at each of itsoutput terminals 24, V_(p), pε{a, b, c}, with respect to the supplyground 26, N. The output terminals 24 are connected to the load 16,which comprises load inductor L_(l) in series with a load resistor R_(l)and the grid voltage V_(g,p).

FIG. 2 shows a converter module 22 or converter cell 22 of the modularconverter 10. The converter module comprises two semiconductor switches28 connected in series, which are connected in parallel to twofree-wheeling diodes 30 and to a capacitor 32. It is also possible toincorporate the functionality of the free-wheeling diode into thesemiconductor switch.

Each converter module 22 acts as a chopper cell with the capacitor 32,C_(pq). Each converter module 22 has two switching states, u_(pq)ε{0,1},where 1 means that the capacitor is connected to the branch 20, i.e. theupper switch 28, S_(pq,T) is turned on. The operation of the twoswitches 28 is complementary to one another. A resistor R_(cap) is shownin parallel to the capacitor 32 to model the leakage current of thecapacitor 32.

Thus each converter module 22 comprises two power connectors, at leasttwo power semiconductors 28 and the capacitor 32, wherein the powerconnectors are short-circuited in a first switching state of thesemiconductors and are connected to the capacitor in a second switchingstate of the semiconductors 28.

FIG. 3 schematically shows a controller 40 for the modular converter 10.The controller 40 comprises three controller stages 42, 44, 46, i.e. anupper (current) controller 42, a modulator 44 and a lower (balancing)controller 46.

The operation of the controller 40 will be explained with reference toFIG. 4, which shows a flow diagram for controlling the modular converter10.

In step 60, the controller 42 receives a controller input referencevector 48 in the form of a current reference vector 48, i*, a controllerinput vector 50 in the form of a current vector 50, i and a controllerinput parameter vector 51 in the form of a parameter vector 51, v_(p).For example, the current vector 50 comprises one or more actual currentsmeasured in the circuit of the modular converter 10 or estimated fromother quantities measured in the circuit of the converter 10.

In steps 62, 64, 66, the controller 42 determines a control outputreference vector 52 in the form of a voltage reference vector 52 fromthe control input reference vector 48, the control input vector 50 andthe control input parameter vector 51. Steps 60, 62, 64 will beexplained in the following in more detail.

In step 68, a voltage vector 54 is derived from the control outputvector 52. For example, an optional modulator 44 may perform apulse-width modulation method or a space vector modulation method forgenerating a voltage vector 54 from the voltage reference vector 52.

Alternatively, the voltage vector 54 may be determined based on arounding of the control output vector 52. For example, for asufficiently large number of converter modules 22 per branch 20, themodulator 44 may be replaced by a simple rounding scheme. Such arounding scheme may round a real-valued branch voltage to an integernumber, corresponding to the number of converter modules 22 per branch20 being turned on.

In step 70, the balancing controller 46 directly controls the convertermodules 22 by generating switching or gating signals 56 for the switches28 from the voltage vector 54.

FIG. 5 shows a prediction model 80 for the modular converter 10, whichis used in step 62 to predict future states of the modular converter 10.

In general, the prediction model 80 may model a part of the circuitry ofthe modular converter 10 and the load 16. For example, with Kirchhoff'slaws, equations may be derived from the circuitry of the converter 10that present a part of the prediction model 80.

Furthermore, the converter modules 22 of one branch 20 may be treated asa voltage source 82 that has to be regulated by the controller 40.

For example, for the topology shown in FIG. 1, the output equations forthe load current in phases a, b and c are as follows:

i _(a)(t)=i _(aP)(t)−i _(aN)(t)

i _(b)(t)=i _(bP)(t)−i _(bN)(t)

i _(c)(t)=i _(aP)(t)−i _(aN)(t)−i _(bP)(t)+i _(bN)(t)

The equation which defines the circulating currents in phases a, b and cis as follows:

${{i_{{cir},p}(t)} = {\frac{i_{pP}(t)}{2} + \frac{i_{pN}(t)}{2} - \frac{i_{dc}}{3}}},{p \in \left\{ {a,b,c} \right\}}$

These state equations may be derived by applying Kirchhoff's voltage lawaround the five circuit meshes of the circuit shown in FIG. 1. Note thatthese equations are independent from the number of converter modules 22in one branch 20.

The model state vector x=[i_(aP) i_(aN) i_(bP) i_(bN) i_(dc)]^(T) of theprediction model 80 includes the upper branch currents i_(aP), i_(aN)and the lower branch currents i_(bP), i_(bN) of phase legs a and b, aswell as the DC link current i_(dc).

The model input vector u=[v_(aP) v_(aN) V_(bP) V_(bN) V_(cP)V_(cN)]^(T)εR⁶ of the prediction model 80 comprises the six branchvoltages v_(aP), v_(aN), v_(bP), v_(bN), v_(cP), v_(cN), which areassumed to be real-valued.

The three-phase grid voltage v_(ga), v_(gb), v_(gc) of the load 16 andthe DC link voltage v_(dc) constitute the parameter vector v_(p)=[v_(ga)v_(gb) v_(gc) v_(dc)]^(T) of the prediction model 80.

The model output vector y has five elements. One choice is to use twoload currents, either i_(a) and i_(b), or i_(α) and i_(β), i.e. the loadcurrents represented in the stationary orthogonal coordinate system,along with the three circulating currents i_(cir,a), i_(cir,b),i_(cir,c). An alternative choice for the model output vector y is to usethe five branch currents of the model state vector x.

In general, the state of the modular converter 10 may be modeled withthe branch currents i_(aP), i_(aN), i_(bP), i_(bN), i_(cP), i_(cN), thebranch voltages v_(aP), v_(aN), v_(bP), V_(bN), v_(cP), v_(cN), the DClink current i_(dc), the DC link voltage v_(dc), the output currentsi_(a), i_(b), i_(c), and the grid voltages v_(ga), v_(gb), v_(gc) of theload 16. However, these quantities are not independent from each other.

FIG. 6 shows the evolution of the state of the modular converter 10 overthe time t, which is depicted to the right. FIG. 6 shows the past 90 tothe left of the y-axis, and a prediction horizon 92 to the right of they-axis.

For example, a prediction model 80 may use a discrete time state-spacerepresentation with discrete time steps k. Then from an actual state 94at time step k, a sequence of future states 96 is predicted for the timesteps k+1 to k+N, where N is the length of the prediction horizon 92.

In particular, FIG. 6 schematically shows the predicted sequence 98 ofmodel output vectors y and the predicted sequence 100 of model inputvectors u for the time steps k to k+N−1.

For the topology shown in FIG. 1 and FIG. 5, a prediction model 80 ofthe following form can be derived. Note that the B₁-matrix istime-varying, since it includes the voltages of the capacitor 32 of thebranch modules 22.

x(k+1)=Ax(k)+B ₁(k)u(k)+B ₂ v _(p)(k)y(k+1)=Cx(k+1)

This model assumes that the voltages of the capacitors 32 exhibit minorvariations within the time-frame of the prediction horizon 92.

However, if the prediction horizon 92 is long and/or the capacitors 32are relatively small, it may be beneficial to explicitly model thevoltage variations of the capacitors 32. This may be done by extendingthe model state vector x by adding the sum of the capacitor voltages ofthe branches 20. The resulting prediction model 80 is of first order.

The evolution of the grid voltages may be included in the predictionmodel 80, by adding the two states v_(gα) and v_(gβ) to the model statevector x and by modeling the rotation of the grid voltage vector, whoserotational speed is proportional to the grid frequency.

In general, the prediction model 80 is adapted for calculating futurestates 96 of the modular converter 10 based on an actual state 94 of themodular converter.

It has to be noted that the prediction model 80 may be formulated indifferent coordinate systems, including abc, aβ or dq, or a combinationthereof.

In step 64, the predicted future states 96 are optimized with respect toan objective function. It has to be noted, that the steps 62 and 64 maybe performed in one operation by numerically solving a mathematicalprogramming problem defined by matrix equations, further constraints andthe objective function.

The objective function associates a scalar performance index withdifferent predicted scenarios, i.e. the objective function is areal-valued function of the states and control actions of the modularconverter 10.

Typically, the objective function includes penalties on the predictedevolution of the tracking error and the (change in the) control effortover the prediction horizon N.

${J\left( {x(k)} \right)} = {{\sum\limits_{l = k}^{k + N - 1}\; {{{y^{*}(l)} - {y(l)}}}_{Q}^{2}} + {{{u(l)} - {u\left( {l - 1} \right)}}}_{R}^{2}}$

Note that in the above defined model, y* denotes the time-varyingcurrent reference vector. The matrices Q and R constitute penaltymatrices on the current error and the change in the manipulatedvariable.

In particular, the objective function is based on differences betweenthe control input reference vector 48 at time step l and the evolutionof the control input vector 50 at time step l. Additionally, theobjective function optimizes a cost value associated with switchingcosts of the converter modules 10 by minimizing the differences betweenthe model input vectors u at time step l and time step l-I.

The objective function is minimized subject to the evolution of theprediction model 80 from time-step k until k+N−1. Moreover, constraintson the currents, which are included in x and y, may be included, as wellas constraints on u. Upper and lower constraints as well as rateconstraints can be considered. Since the state-space model is linear,the cost function is quadratic and the constraints are linear, theresulting optimization problem is a so-called quadratic program (QP).The QP can be formulated and solved efficiently, e.g. by using an activeset method or a fast gradient search method.

The result of the optimization step 64 is the sequence 100 of optimalmodel control inputs U=[u^(T)(k)u^(T)(k+1) . . . u^(T)(k+N−1)]^(T) attime-step k.

In step 66, the controller 42 determines the control output referencevector 52 from the sequence 100 of future control actions by taking thefirst element u(k) of the first model input vector u at time step k. Thefirst element u(k) is the output reference vector 52.

Only the first element u(k) of the sequence 100 of optimal controlinputs is implemented at time-step k and sent to the controller 44. Atthe next time-step k+1, new measurements (or estimates) are obtained andthe optimization problem is solved again over a shifted predictionhorizon 92. This so-called receding horizon policy provides feedback andensures that the controller 42 is robust to parameter uncertainties.

Further embodiments of the control method are explained in thefollowing:

A time delay caused by the computation of the control output referencevector 52 may be compensated for. This time delay typically amounts tothe length of one sampling interval. By using the last control input andthe model state vector x(k) at time step k, the model state vectorx(k+1) at time step k+1 may be predicted, for which the prediction model80 is solved.

In step 64, a (piecewise) linear (instead of a quadratic) cost functionmay be used, for example based on absolute values and/or maximal values,leading to a linear program (LP) instead of a QP.

In step 62, additional control loops may be added. For example, in step62 the occurrence of faults, loss of modules, voltage dips, loadimbalances, disturbances and/or grid (or load) asymmetries, etc. may bemonitored. If a fault or asymmetry is detected, the controller 42adjusts its control actions so as to accommodate for this event withinthe physical limits, providing automatic controller reconfiguration. Forexample, the prediction model 80 is updated to a new topology takinginto account the fault or asymmetry.

When modeling the prediction model 80, a higher order load system 16 maybe considered, including AC machines, grids with transformers and loadswith filters. To address such higher order systems, the prediction model80, the model state vector x, the parameter vector v_(p) and the outputvector y may be augmented accordingly.

While the invention has been illustrated and described in detail in thedrawings and foregoing description, such illustration and descriptionare to be considered illustrative or exemplary and not restrictive; theinvention is not limited to the disclosed embodiments. Other variationsto the disclosed embodiments can be understood and effected by thoseskilled in the art and practising the claimed invention, from a study ofthe drawings, the disclosure, and the appended claims. In the claims,the word “comprising” does not exclude other elements or steps, and theindefinite article “a” or “an” does not exclude a plurality. A singleprocessor or controller or other unit may fulfil the functions ofseveral items recited in the claims. The mere fact that certain measuresare recited in mutually different dependent claims does not indicatethat a combination of these measures cannot be used to advantage. Anyreference signs in the claims should not be construed as limiting thescope.

1. A method for controlling a modular converter, the modular converterincluding a plurality of converter modules configured for converting aninput voltage into an output voltage to be supplied to a load, themethod comprising: receiving a control input reference vector, a controlinput vector and a control input parameter vector; determining a controloutput reference vector from the control input reference vector, thecontrol input vector and the control input parameter vector in a firstcontrol stage; and controlling the converter modules by generatingswitching signals based on the control output reference vector in afurther control stage; wherein the control output reference vector isdetermined by: predicting at least one future state of the modularconverter with a prediction model of the modular converter, wherein theprediction model is adapted for calculating the future state of themodular converter based on an actual state of the modular converter, astate of the modular converter having current values and/or voltagevalues of the modular converter; enhancing the at least one future statewith respect to an objective function, wherein the objective function isbased on a cost value associated with switching costs of the convertermodules; and determining the control output reference vector from thefuture state.
 2. The method of claim 1, wherein the modular convertercontrolled by the method is a modular multi-level converter wherein eachconverter module of the modular multi-level converter includes two powerconnectors, at least two power semiconductors and a capacitor, whereinthe power connectors are short-circuited in a first switching state ofthe power semiconductors and are connected to the capacitor in a secondswitching state of the power semiconductors.
 3. The method of claim 1,comprising: determining a voltage vector from the control outputreference vector in a second control stage with a modulator; andcontrolling the converter modules by generating switching signals fromthe voltage vector in a third control stage.
 4. The method of claim 1,wherein the control input reference vector is a current referencevector, the control input vector is an actual current vector and thecontrol input parameter vector is an actual voltage vector; and/orwherein the control output reference vector is a voltage referencevector.
 5. The method of claim 1, wherein a sequence of future states ispredicted for a plurality of time steps in the future; and wherein thecontrol output reference vector is determined from a next future stateassociated with a next time step.
 6. The method of claim 1, wherein theprediction model is based on linear equations relating voltages and/orcurrents at a time step with voltages and/or currents at a next timestep.
 7. The method of claim 1, wherein the prediction model includes amodel of the converter modules and/or a model of the load.
 8. The methodof claim 1, comprising: compensating a time delay caused by thedetermining of the control output reference vector by predictingcurrents at a next time step using actual voltages and/or currents. 9.The method of claim 1, wherein the objective function minimizes a changein evolution of the control output reference vector.
 10. The method ofclaim 1, wherein the objective function is based on a vector norm. 11.The method of claim 1, wherein the objective function is based on aquadratic and/or linear norm.
 12. The method of claim 1, comprising:controlling the converter modules by generating switching signals from arounded control output reference vector.
 13. The method of claim 1,comprising: detecting a converter module with a fault; short-circuitingthe detected converter module; and removing the short-circuitedconverter model from the prediction model.
 14. A controller forcontrolling a modular converter, wherein the controller is configuredfor performing the steps of: predicting at least one future state of themodular converter with a prediction model of the modular converter,wherein the prediction model is adapted for calculating the future stateof the modular converter based on an actual state of the converter, astate of the modular converter having current values and/or voltagevalues of the modular converter; enhancing the at least one future statewith respect to an objective function, wherein the objective is based ona cost value associated with switching costs of converter modules of themodular converter; and determining a control output reference vectorfrom the future state.
 15. A modular converter for supplying a load withelectrical voltages, the modular converter comprising: a plurality ofconverter modules having semiconductor switches and a capacitor; a firstcontroller according to claim 14 for generating a control outputreference vector; and a further controller for generating switchingsignals for the converter modules based on the control output referencevector.
 16. The modular converter of claim 15, wherein the modularconverter is a modular multi-level converter.
 17. The method of claim 2,comprising: determining a voltage vector from the control outputreference vector in a second control stage with a modulator; andcontrolling the converter modules by generating switching signals fromthe voltage vector in a third control stage.
 18. The method of claim 17,wherein the control input reference vector is a current referencevector, the control input vector is an actual current vector and thecontrol input parameter vector is an actual voltage vector; and/orwherein the control output reference vector is a voltage referencevector.
 19. The method of claim 18, wherein a sequence of future statesis predicted for a plurality of time steps in the future; and whereinthe control output reference vector is determined from a next futurestate associated with a next time step.
 20. The method of claim 19,wherein the prediction model is based on linear equations relatingvoltages and/or currents at a time step with voltages and/or currents ata next time step.